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The Method of Integrating Factors Examples 2

Recall from The Method of Integrating Factors page that we can solve first order linear differential equations of the form $\frac{dy}{dt} + p(t) y = g(t)$ by multiplying both sides of the equation by the integrating factor $\mu (t) = e^{\int p(t) \: dt}$ so that:

Example 2

We want to rewrite the differential equation above so that it is in the correct form to apply the method of integrating factors. If we divide both sides of the differential equation above by $(t^2 - 1)$ we get that: